We asked some traffic experts at LA Metro and CalTrans. Their explanation:

There may be many reasons, but the biggest one is that in the morning, people usually have a single destination in mind: getting to school or work. In the evening, people leave work at different times, and often run errands, go to dinner, shop, etc., driving more total miles.

How we did it: We divided the Los Angeles freeway system into nine different segments. For example, we looked at the 5 freeway from the 10 near downtown till it intersects with the 605 freeway. We also looked at another segment of the 5 between the 10, heading north till it stretches to the edge of Santa Clarita. We did this for seven other freeway segments.

continued…Then, we divided each section into two directions (e.g., east and west on the 10, or north and south on the 5). With the TRANSDEC database, we were able to calculate the average speed in each directions for every hour for 12 months.

continued…Then, we narrowed that down to just the average morning and evening rush hour speeds on each section and compared their speeds in each direction. Morning rush hour is 7-9 am; evening rush hour is 4-7 pm. We compared the morning rush hour speed on a section of the 5 freeway heading south against the evening rush hour speed heading north on the same route. We looked at 18 round-trip freeway commutes in total.
In order to validate the results, we checked our conclusions with LA Metro and CalTrans.